The Biden administration has offered to free the imprisoned Russian arms dealer Viktor Bout to secure the release of Brittney Griner and Paul N. Whelan, two Americans imprisoned in Russia who the State Department says were wrongfully detained, according to a person familiar with the negotiations.

Secretary of State Antony J. Blinken said Wednesday that the United States had “put a substantial proposal on the table” and that he would soon press for the Americans’ return in his first conversation with his Russian counterpart since Russia invaded Ukraine five months ago.

Mr. Blinken’s comments represented the first time that the United States had confirmed that it had made a formal proposal to persuade Russia to release Ms. Griner, an American basketball star who has been detained for months on drug charges, and Mr. Whelan, a former U.S. Marine who was sentenced in Russia in 2020 to 16 years in prison on espionage charges.